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Enumeration of certain subsets of uprooted trees and spherical parking functions
Nayana Shibu Deepthi, Chanchal Kumar, Gargi Lather
Spherical -parking functions are a distinguished subset of standard monomials, arising from the skeleton ideals of the -parking function ideal. Explicit enumeration formulas…
On Very Generic Discriminantal Arrangements
C P Anil Kumar
In this article we prove two main results. Firstly, we show that any six-line arrangement, consisting of three pairs of mutually perpendicular lines, does not give rise to a "very…
Standard Monomials of 1-Skeleton Ideals of Graphs and Their Signless Laplace Matrices
Chanchal Kumar, Gargi Lather, Amit Roy
Let be a (multi) graph on the vertex set with root . The -parking function ideal is a monomial ideal in the polynomial ring $R=\math…
Skeleton Ideals of Certain Graphs, Standard Monomials and Spherical Parking Functions
Chanchal Kumar, Gargi Lather, Sonica
Let be an (oriented) graph on the vertex set with root . Postnikov and Shapiro associated a monomial ideal in the polynomial ring $…
Integer Sequences and Monomial Ideals
Chanchal Kumar, Amit Roy
Let be the set of all permutations of and let be the subset consisting of permutations avoiding 132 and 312-patterns…
A Combinatorial Identity for the p-Binomial Coefficient Based on Abelian Groups
C P Anil Kumar
For non-negative integers , we prove a combinatorial identity for the -binomial coefficient based on abelian p-groups. A purely combinatorial proof of…